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visual3d:documentation:modeling:segments:segment_inertia [2024/09/28 02:10] – Cleaned up page formatting and organization. wikisysopvisual3d:documentation:modeling:segments:segment_inertia [2026/06/03 19:25] (current) – Updated header levels. wikisysop
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-===== Segment Inertia =====+====== Segment Inertia ======
  
 Visual3D computes the moment of inertia of a segment from the segment's mass, proximal and distal radii, and [[Visual3D:Documentation:Modeling:Segments:Segment_Geometry|geometry]]. The default Visual3D segments are treated as [[Visual3D:Documentation:Modeling:Segments:Segment_Geometry|geometric objects]] that have inertial properties based on their shape in accordance with Hanavan's mathematical model of the human body. Visual3D computes the moment of inertia of a segment from the segment's mass, proximal and distal radii, and [[Visual3D:Documentation:Modeling:Segments:Segment_Geometry|geometry]]. The default Visual3D segments are treated as [[Visual3D:Documentation:Modeling:Segments:Segment_Geometry|geometric objects]] that have inertial properties based on their shape in accordance with Hanavan's mathematical model of the human body.
  
-==== Inertial properties of a Cone (Conical Frustrum) ====+===== Inertial properties of a Cone (Conical Frustrum) =====
  
 Visual3D's **Cone** segment geometry is, to be precise, a **conical frustrum.** A **frustra of right cones** is created by cutting the top off of a cone such that the cut is parallel to the base of the cone. Visual3D's **Cone** segment geometry is, to be precise, a **conical frustrum.** A **frustra of right cones** is created by cutting the top off of a cone such that the cut is parallel to the base of the cone.
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 {{:frustraOfRightCones2.png}} {{:frustraOfRightCones2.png}}
  
-A Cone segment with mass M and length L has the following inertial properties:+A cone segment with mass M and length L has the following inertial properties:
  
 {{:FrustraOfRightCones3.jpg}}\\ {{:FrustraOfRightCones3.jpg}}\\
  
-==== Inertial properties of an Elliptical Cylinder ====+===== Inertial properties of an Elliptical Cylinder =====
  
 Visual3D's **Cylinder** segment geometry is a right elliptical cylinder, which is a cylinder with elliptical cross-sections. Visual3D's **Cylinder** segment geometry is a right elliptical cylinder, which is a cylinder with elliptical cross-sections.
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 Note that Visual3D uses the radius at the distal end of the segment as the radius of the cylinder. Note that Visual3D uses the radius at the distal end of the segment as the radius of the cylinder.
  
-==== Inertial Properties of a Sphere ====+===== Inertial Properties of a Sphere =====
  
 For segments modelled as a **Sphere**, Visual3D requires a proximal segment radius and a distal segment radius. The inertial properties of the segment are calculated using only the distal radius, however, the proximal radius is still required to determine the location of the proximal segment end. For segments modelled as a **Sphere**, Visual3D requires a proximal segment radius and a distal segment radius. The inertial properties of the segment are calculated using only the distal radius, however, the proximal radius is still required to determine the location of the proximal segment end.
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 Note that Visual3D uses the radius at the distal end of the segment as the radius of the sphere. The length of the sphere is determined from the distance between the segment's proximal and distal ends. Note that Visual3D uses the radius at the distal end of the segment as the radius of the sphere. The length of the sphere is determined from the distance between the segment's proximal and distal ends.
  
-==== Inertial Properties of an Ellipsoid ====+===== Inertial Properties of an Ellipsoid =====
  
 Visual3D also allows segments to be defined as an **Ellipsoid**, or deformed sphere. Visual3D also allows segments to be defined as an **Ellipsoid**, or deformed sphere.
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 Visual3D uses the radius at the distal end of the segment as the radius of the ellipsoid. The length of the ellipsoid is calculated as tghe distance between the sgement's proximal and distal ends. Visual3D uses the radius at the distal end of the segment as the radius of the ellipsoid. The length of the ellipsoid is calculated as tghe distance between the sgement's proximal and distal ends.
  
-==== Alternative Approaches ====+===== Alternative Approaches =====
  
 The user is free to modify segment characteristics away from Visual3D's defaults for both inertial parameters and coordinate systems. The user is free to modify segment characteristics away from Visual3D's defaults for both inertial parameters and coordinate systems.
  
-=== Adjusted Zatsiorsky-Seluyanov's segment inertia parameters ===+==== Adjusted Zatsiorsky-Seluyanov's segment inertia parameters ====
  
 It is possible to use the [[visual3d:documentation:definitions:adjusted_zatsiorsky-seluyanov_s_segment_inertia_parameters|Adjusted Zatsiorsky-Seluyanov's segment inertia parameters]] in Visual3D instead of the default parameters from Dempster and Hanavan. It is possible to use the [[visual3d:documentation:definitions:adjusted_zatsiorsky-seluyanov_s_segment_inertia_parameters|Adjusted Zatsiorsky-Seluyanov's segment inertia parameters]] in Visual3D instead of the default parameters from Dempster and Hanavan.
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 These inertial parameters adjust the original Zatsiorsky-Seluyanov segment inertia parameters from using bony landmarks as reference points to  using joints centres instead since these more commonly used in biomechanics. These inertial parameters adjust the original Zatsiorsky-Seluyanov segment inertia parameters from using bony landmarks as reference points to  using joints centres instead since these more commonly used in biomechanics.
  
-=== Entering Inertial Values Using Expressions ===+==== Entering Inertial Values Using Expressions ====
  
 Visual3D allows the user to put [[visual3d:documentation:pipeline:expressions:expressions_overview|expressions]] into the edit boxes, which means that any mathematical expression or regression equation can be used to express a segment's inertial properties and center of mass. Visual3D allows the user to put [[visual3d:documentation:pipeline:expressions:expressions_overview|expressions]] into the edit boxes, which means that any mathematical expression or regression equation can be used to express a segment's inertial properties and center of mass.
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 See the page covering [[Visual3D:Documentation:Pipeline:Force_Commands:Entering_Inertial_Values_Using_Expressions|entering inertial values using expressions]] for more details. See the page covering [[Visual3D:Documentation:Pipeline:Force_Commands:Entering_Inertial_Values_Using_Expressions|entering inertial values using expressions]] for more details.
  
-=== Coordinate System Transformations ===+==== Coordinate System Transformations ====
  
 Visual3D allows users to flexibly express a segment's moment of inertia in any coordinate system. See the page on [[Visual3D:Documentation:Modeling:Segments:Transforming_Segment_Moment_of_Inertia|transforming segment moments of inertia]] for complete details. Visual3D allows users to flexibly express a segment's moment of inertia in any coordinate system. See the page on [[Visual3D:Documentation:Modeling:Segments:Transforming_Segment_Moment_of_Inertia|transforming segment moments of inertia]] for complete details.
  
-==== References ====+===== References =====
  
    * Hanavan E. (1964) A Mathematical Model for the Human Body. Technical Report, Wright-Patterson Air Force Base    * Hanavan E. (1964) A Mathematical Model for the Human Body. Technical Report, Wright-Patterson Air Force Base
  
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